8.7: Chapter 8 Key Terms and Symbols

Introductory Statistics OER - Exercise Questions Each Section Included · LibreTexts

0%

Contents

    Text

    Size
    100%
    Theme
    Typeface
    Line length
    Spacing

    From LibreTexts, under CC BY 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    ↵

    Glossary of Key Terms and Symbols

    Key Terms

    Alternative Hypothesis (H₁): The statement that there is an effect or a difference; it is the logical complement of H₀.

    Confidence Level (1 − α): The probability that the confidence interval contains the true population parameter.

    Critical Value Method: A traditional approach where the test statistic is compared to a cutoff value from the z or t distribution.

    Hypothesis Testing: A method for making decisions about population parameters using sample data.

    Null Hypothesis (H₀): The assumption that there is no effect or no difference. It is assumed true until evidence suggests otherwise.

    One-Sample t-Test for the Mean: Used when the population standard deviation is unknown and the sample is drawn from a normally distributed population.

    One-Sample z-Test for a Proportion: Used to test a claim about a population proportion when the sample size is large enough to satisfy normal approximation conditions.

    One-Sample z-Test for the Mean: Used when the population standard deviation is known and the sample size is large or the population is normally distributed.

    Parameter: A numerical measure that describes a characteristic of a population (e.g., population mean or proportion).

    p-Value Method: A modern approach that calculates the probability of the observed sample result under H₀. If the p-value is less than α, H₀ is rejected.

    Significance Level (α): The probability of making a Type I Error, or rejecting H₀ when it is true. Common values are 0.05 or 0.01.

    Statistic: A numerical measure that describes a characteristic of a sample, used to estimate a population parameter.

    Statistical Hypothesis: A claim or conjecture about a population parameter that can be tested with sample data.

    Test Statistic: A standardized value (z or t) used to decide whether to reject H₀. It compares the sample result to the expected result under H₀.

    Type I Error (α): Rejecting H₀ when H₀ is true.

    Type II Error (β): Failing to reject H₀ when H₀ is false.

    Key Symbols

    \( H_0 \) - Null hypothesis.

    \( H_1 \) - Alternative hypothesis.

    \( \alpha \) - Significance level (probability of a Type I error).

    \( \beta \) - Probability of a Type II error.

    \( \bar{x} \) - Sample mean.

    \( \mu \) - Population mean.

    \( p \) - Population proportion.

    \( \hat{p} \) - Sample proportion.

    \( n \) - Sample size.

    \( \sigma \) - Population standard deviation.

    \( s \) - Sample standard deviation.

    \( z \) - Test statistic for z-tests (when population standard deviation is known).

    \( t \) - Test statistic for t-tests (when population standard deviation is unknown).

    \( z_{\alpha/2} \) - Critical z-value for two-tailed tests.

    \( t_{\alpha/2} \) - Critical t-value for two-tailed tests.
    p-value - Probability of observing the test result under the assumption that \( H_0 \) is true.

    SE - Standard error (standard deviation of the sampling distribution).

    This page titled 8.7: Chapter 8 Key Terms and Symbols was last modified on Wed, 20 Aug 2025 23:55:26 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Toros Berberyan, Tracy Nguyen, and Alfie Swan.